. A professor has RM 15000 to invest for one year, some are 8% and the rest are at 7% annual interest. If she will earn RM 1100 from these investments, how much did she invest at each rate?
At 8%, she gets RM1200.
At 7%, she gets RM1050.
Let x be the fraction he invested at 8%, the 1-x is what he invested at 7%.
we have
x*1200+(1-x)1050=1100
Solve for x.
10
hint: x=1/3
To solve this problem, we can use a system of equations. Let's assume that the professor invested an amount of money, x, at an 8% annual interest rate, and the remaining amount, 15000 - x, at a 7% annual interest rate.
The equation representing the interest earned from the 8% investment can be written as:
0.08x (interest rate multiplied by the amount invested)
The equation representing the interest earned from the 7% investment can be written as:
0.07(15000 - x) (interest rate multiplied by the amount invested)
According to the problem, the total interest earned is RM 1100. Therefore, we can set up the following equation:
0.08x + 0.07(15000 - x) = 1100
Now, we can solve this equation to find the values of x, which represents the amount invested at 8%, and (15000 - x), which represents the amount invested at 7%.
0.08x + 0.07(15000 - x) = 1100
0.08x + 1050 - 0.07x = 1100
0.01x = 50
x = 5000
Therefore, the professor invested RM 5000 at an 8% annual interest rate and the remaining amount, (15000 - 5000) = RM 10000, at a 7% annual interest rate.